The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

We present theoretical studies of helium droplets and films doped with one electronically excited rubidium atom Rb ‫ء‬ ͑ 2 P͒. Diffusion and path integral Monte Carlo approaches are used to investigate the energetics and the structure of clusters containing up to 14 helium atoms. The surface of large clusters is approximated by a helium film. The nonpair additive potential energy surface is modeled using a diatomic in molecule scheme. Calculations show that the stable structure of Rb ‫ء‬ He n consists of a seven helium atom ring centered at the rubidium, surrounded by a tirelike second solvation shell. A very different structure is obtained when performing a "vertical Monte Carlo transition." In this approach, a path integral Monte Carlo equilibration starts from the stable configuration of a rubidium atom in the electronic ground state adsorbed to the helium surface after switching to the electronically excited surface. In this case, Rb ‫ء‬ He n relaxes to a weakly bound metastable state in which Rb ‫ء‬ sits in a shallow dimple. The interpretation of the results is consistent with the recent experimental observations ͓G. Auböck et al., Phys. Rev. Lett. 101, 035301 ͑2008͔͒.

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“…It is described in detail in Ref. 42. Finally, a Metropolis step based on the trial function ⌿ T is added at each time step.…”

Section: ‫ץ‬ F͑x͒mentioning

confidence: 99%

Electronically excited rubidium atom in a helium cluster or film

Leino

Viel

Zillich

2008

The Journal of Chemical Physics

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“…Some recent examples are computation of the zero-point energy and tunneling splitting in malonaldehyde 5 and diffusion Monte Carlo study of CH 5 + . 6 Imaginary-time evolution also appears in computation of correlation functions for complex systems in a Boltzmann ͑thermal͒ distribution, 7 such as the reaction rate constants within the thermal flux operator approach.…”

Section: Introductionmentioning

confidence: 99%

Quantum trajectory dynamics in imaginary time with the momentum-dependent quantum potential

Garashchuk

2010

The Journal of Chemical Physics

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The quantum trajectory dynamics is extended to the wave function evolution in imaginary time. For a nodeless wave function a simple exponential form leads to the classical-like equations of motion of trajectories, representing the wave function, in the presence of the momentum-dependent quantum potential in addition to the external potential. For a Gaussian wave function this quantum potential is a time-dependent constant, generating zero quantum force yet contributing to the total energy. For anharmonic potentials the momentum-dependent quantum potential is cheaply estimated from the global Least-squares Fit to the trajectory momenta in the Taylor basis. Wave functions with nodes are described in the mixed coordinate space/trajectory representation at little additional computational cost. The nodeless wave function, represented by the trajectory ensemble, decays to the ground state. The mixed representation wave functions, with lower energy contributions projected out at each time step, decay to the excited energy states. The approach, illustrated by computing energy levels for anharmonic oscillators and energy level splitting for the double-well potential, can be used for the Boltzmann operator evolution.

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“…The expectation values are evaluated according to Eq. (18). Equation (17) will be used to approximate MDQP (and other terms containing spatial derivatives of p) needed in the Eulerian and in the modified Lagrangian dynamics described below.…”

Section: A Formalismmentioning

confidence: 99%

“…exact QM calculations of the zero-point energies (ZPEs) using the diffusion Monte Carlo. [15][16][17][18][19] Thus, for any initial ψ the wavefunction energy E converges to the ZPE value, E 0 , in the course of evolution,…”

Section: Introductionmentioning

confidence: 99%

Efficient quantum trajectory representation of wavefunctions evolving in imaginary time

Garashchuk

Mazzuca

Vazhappilly

2011

The Journal of Chemical Physics

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The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential -computed approximately to be practical in high-dimensional systems -influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]. For a nodeless wavefunction represented as ψ(x, t) = exp(−S(x, t)/¯) with the trajectory momenta defined by ∇ S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and time-dependent components into the wavefunction representation generates new Lagrangian-type dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zero-point energy of a strongly anharmonic well and low-lying eigenstates of a high-dimensional coupled harmonic system.

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The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Cited by 68 publications

References 76 publications

Electronically excited rubidium atom in a helium cluster or film

Electronically excited rubidium atom in a helium cluster or film

Quantum trajectory dynamics in imaginary time with the momentum-dependent quantum potential

Efficient quantum trajectory representation of wavefunctions evolving in imaginary time

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